Terrain-Following Coordinate Transformation

From the point of view of the computational model, it is highly
convenient to introduce a stretched vertical coordinate system which
essentially "flattens out" the variable bottom at z=−h(x,y).
Such "σ" coordinate systems have long been used, with slight
appropriate modification, in both meteorology and oceanography
[e.g., Phillips (1957) and Freeman et al. (1972)].
To proceed, we make the coordinate transformation: